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Toward quantum simulating non-Abelian gauge theories

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Abstract

In this article, we review some of the recent developments toward the future goal of quantum computing or quantum simulating lattice-QCD. This includes a novel theoretical framework developed for non-Abelian gauge theories that is the first necessary step toward this goal. We also review some immediate applications of this framework in the context of both digital and analog quantum simulations of SU(2) lattice gauge theory coupled with staggered fermions.

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Notes

  1. For general SU(N) with \(N>2\), these will be the generalized Gell-Mann matrices \(\lambda ^a\), generating the Lie algebra associated with the special unitary group SU(N). For the specific case of SU(3), the \(3\times 3\) standard Gell-Mann matrices would play the same role

References

  1. C Quigg Gauge Theories of the Strong, Weak, and Electromagnetic Interactions (Princeton: Princeton University Press, 2013)

    MATH  Google Scholar 

  2. W Marciano and H Pagels Phys. Rep. 36 137 (1978). https://www.sciencedirect.com/science/article/pii/0370157378902089

  3. K G Wilson Phys. Rev. D 10 2445 (1974). https://link.aps.org/doi/10.1103/PhysRevD.10.2445

  4. M Creutz, L Jacobs and C Rebbi Phys. Rep. 95 201 (1983). http://www.sciencedirect.com/science/article/pii/0370157383900169

  5. B Joó, C Jung, N H Christ, W Detmold, R G Edwards, M Savage and P Shanahan Eur. Phys. J. A 55 199 (2019)

    Article  ADS  Google Scholar 

  6. P De Forcrand, arXiv preprint arXiv:1005.0539 (2010)

  7. R P Feynman Int. J. Theor. Phys. 21(6/7) (1982)

  8. F Arute et al. Nature 574 505 (2019)

    Article  ADS  Google Scholar 

  9. D Castelvecchi Nat. News 543 159 (2017)

    Article  Google Scholar 

  10. J Preskill Quantum 2 (2018)

    Article  Google Scholar 

  11. I Buluta and F Nori Science 326 108 (2009)

    Article  ADS  Google Scholar 

  12. M Bañuls et al Eur. Phys. J. D 74 165 (2020). https://doi.org/10.1140/epjd/e2020-100571-8

  13. E Zohar, J Cirac and B Reznik Phys. Rev. Lett. 110 125304 (2013). https://doi.org/10.1103/PhysRevLett.110.125304

  14. D Banerjee, M Dalmonte, M Muller, E Rico, P Stebler, U J Wiese and P Zoller Phys. Rev. Lett. 109 175302 (2012). https://doi.org/10.1103/PhysRevLett.109.175302

  15. E Zohar, J I Cirac and B Reznik Phys. Rev. A 88 023617 (2013). https://doi.org/10.1103/PhysRevA.88.023617

  16. D Banerjee, M Bögli, M Dalmonte, E Rico, P Stebler, U J Wiese and P Zoller Phys. Rev. Lett. 110 125303 (2013). https://doi.org/10.1103/PhysRevLett.110.125303

  17. E Zohar and M Burrello Phys. Rev. D 91 054506 (2015). https://doi.org/10.1103/PhysRevD.91.054506

  18. E Zohar, J I Cirac and B Reznik Rep. Prog. Phys. 79 014401 (2015)

  19. V Kasper, F Hebenstreit, M Oberthaler and J Berges Phys. Lett. B 760 742 (2016)

    Article  ADS  Google Scholar 

  20. Z Davoudi, M Hafezi, C Monroe, G Pagano, A Seif and A Shaw Phys. Rev. Res. 2 023015 (2020). https://doi.org/10.1103/PhysRevResearch.2.023015

  21. N Klco, E F Dumitrescu, A J McCaskey, T D Morris, R C Pooser, M Sanz, E Solano, P Lougovski and M J Savage Physi. Rev. A 98 032331 (2018)

  22. A F Shaw, P Lougovski, J R Stryker and N Wiebe Quantum 4 306 (2020)

    Article  Google Scholar 

  23. J R Stryker Phys. Rev. A 99 042301 (2019)

  24. B Chakraborty, M Honda, T Izubuchi, Y Kikuchi and A Tomiya, arXiv preprint arXiv:2001.00485 (2020)

  25. E A Martinez, C A Muschik, P Schindler, D Nigg, A Erhard, M Heyl, P Hauke, M Dalmonte, T Monz, P Zoller, et al. Nature 534 516 (2016)

    Article  ADS  Google Scholar 

  26. A Mil, T V Zache, A Hegde, A Xia, R P Bhatt, M K Oberthaler, P Hauke, J Berges and F Jendrzejewski (2019). https://doi.org/10.1126/science.aaz5312

  27. B Yang, H Sun, R Ott, H Y Wang, T V Zache, J C Halimeh, Z S Yuan, P Hauke and J W Pan (2020)

  28. C Schweizer, F  Grusdt, M Berngruber, L Barbiero, E Demler, N Goldman, I Bloch and M Aidelsburger Nat. Phys. 15 1168 (2019)

    Article  Google Scholar 

  29. F Görg, K Sandholzer, J Minguzzi, R Desbuquois, M Messer and T Esslinger Nat. Phys. 15 1161 (2019)

    Article  Google Scholar 

  30. L Tagliacozzo, A Celi, P Orland, M Mitchell and M Lewenstein Nat. Commun. 4 1 (2013)

    Article  Google Scholar 

  31. Z Davoudi, M Hafezi, C Monroe, G Pagano, A Seif and A Shaw Phys. Rev. Res. 2 023015 (2020)

  32. E Zohar and J I Cirac Phys. Rev. D 99 114511 (2019). https://doi.org/10.1103/PhysRevD.99.114511

  33. E Zohar and J I Cirac Phys. Rev. B 98 075119 (2018). https://doi.org/10.1103/PhysRevB.98.075119

  34. J B Kogut and L Susskind Phys. Rev. D 11 395 (1975). https://doi.org/10.1103/PhysRevD.11.395

  35. M Mathur J. Phys. A 38 10015 (2005). https://doi.org/10.1088/0305-4470/38/46/008

  36. M Mathur Nucl. Phys. B 779 32 (2007). https://doi.org/10.1016/j.nuclphysb.2007.04.031

  37. M Mathur, I Raychowdhury and R Anishetty J. Math. Phys. 51 093504 (2010). https://doi.org/10.1063/1.3464267

  38. R Anishetty, M Mathur and I Raychowdhury J. Math. Phys. 50 053503 (2009). https://doi.org/10.1063/1.3122666

  39. R Anishetty, M Mathur and I Raychowdhury J. Phys. A 43 035403 (2010). https://doi.org/10.1088/1751-8113/43/3/035403

  40. R Anishetty and I Raychowdhury Phys. Rev. D 90 114503 (2014). https://doi.org/10.1103/PhysRevD.90.114503

  41. I Raychowdhury, Prepotential Formulation of Lattice Gauge Theories. Ph.D. thesis, Calcutta U. (2013)

  42. I Raychowdhury and R Anishetty PoS LATTICE2014 313 (2014). https://doi.org/10.22323/1.214.0313

  43. I Raychowdhury Eur. Phys. J. C 79 235 (2019). https://doi.org/10.1140/epjc/s10052-019-6753-0

  44. M Mathur, I Raychowdhury and R Anishetty J. Math. Phys. 51 093504 (2010)

  45. I Raychowdhury and J R Stryker Phys. Rev. D 101 114502 (2020). https://doi.org/10.1103/PhysRevD.101.114502

  46. R Anishetty and T Sreeraj Phys. Rev. D 97 074511 (2018)

  47. N Klco, M J Savage and J R Stryker Phys. Rev. D 101 074512 (2020)

  48. S A Rahman, R Lewis, E Mendicelli and S Powell, arXiv preprint arXiv:2103.08661 (2021)

  49. Z Davoudi, I Raychowdhury and A Shaw (2020)

  50. S Chandrasekharan and U J Wiese Nucl. Phys. B 492 455 (1997)

  51. M C Bañuls and K Cichy Rep. Prog. Phys. 83 024401 (2020)

  52. Y Atas, J Zhang, R Lewis, A Jahanpour, J F Haase and C A Muschik, arXiv preprint arXiv:2102.08920 (2021)

  53. I Raychowdhury and J R Stryker Phys. Rev. Res. 2 033039 (2020). https://doi.org/10.1103/PhysRevResearch.2.033039

  54. I Bloch, J Dalibard and S Nascimbene Nat. Phys. 8 267 (2012)

    Article  Google Scholar 

  55. R Blatt and C F Roos Nat. Phys. 8 277 (2012)

  56. R Dasgupta and I Raychowdhury, arXiv preprint arXiv:2009.13969 (2020)

  57. M Messer, R Desbuquois, T Uehlinger, G Jotzu, S Huber, D Greif and T Esslinger Phys. Rev. Lett. 115 115303 (2015)

  58. S Scherg, T Kohlert, J Herbrych, J Stolpp, P Bordia, U Schneider, F Heidrich-Meisner, I Bloch and M Aidelsburger Phys. Rev. Lett. 121 130402 (2018)

  59. A Ciavarella, N Klco and M J Savage Phys. Rev. D.103 094501 (2021)

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Acknowledgements

IR would like to thank Pushan Majumdar for numerous discussions, his encouragement, and enthusiasm toward this emerging field of quantum information science to be applied for lattice gauge theories. IR would also like to mention her sincere gratitude to Pushan Majumdar for his constant support during the difficult period faced by her after having a career break and helping her to return to research career. IR would like thank collaborators Manu Mathur, Ramesh Anishetty, Jesse Stryker, Zohreh Davoudi, Raka Dasgupta for fruitful collaborations at different stages of development toward this research goal. IR would also like to thank David B. Kaplan for direction and support toward this particular research direction. IR is supported by the U.S. Department of Energy (DOE),Office of Science, Office of Advanced Scientific Computing Research (ASCR) Quantum Computing Application Teams (QCAT) program, under fieldwork Proposal No.ERKJ347.

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  1. Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, MD, 20742, USA

    Indrakshi Raychowdhury

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  1. Indrakshi Raychowdhury
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Correspondence to Indrakshi Raychowdhury.

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Raychowdhury, I. Toward quantum simulating non-Abelian gauge theories. Indian J Phys 95, 1681–1690 (2021). https://doi.org/10.1007/s12648-021-02170-6

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